Next we explain how Steps 1 and 2 can be adapted to show
that if \((X,A)\)  has a representation as a \(G\) -fiberwise NDR pair
then \(i\colon A\rightarrow X\)  is an \(\bar{f}\) -cofibration. The usual argument shows that
\(X\times _B\lbrace 0\rbrace \cup A\times _B I\)  is a retract of \(X\times _B I\)  in
\(G{K}/B\) . Hence \(i\colon A\rightarrow X\)  is a closed \(f\) -cofibration in
\(G{K}/B\)  and so \(Mi\rightarrow X\times _B I\)  is the inclusion of a strong
deformation retraction (see Lemma 4.2.5 of [1]}).
The map \(u\)  in a representation \((u,h)\)  of \((X,A)\)  as a \(G\) -fiberwise
NDR pair can be used to show that there exists a map \(\psi \colon X\times _B I\rightarrow I\) 
such that \(\psi ^{-1}(0)= Mi\) . The analogue of Theorem 3
of [2]} for the category \(G{K}/B\)  then shows that \(Mi\rightarrow X\times _B I\) 
has the LLP with respect to all \(f\) -fibrations and hence \(i\colon A\rightarrow X\)  is an \(\bar{f}\) -cofibration.

Finally, let us note ([3]} Lemma 2.6) that since \(\bar{f}\)  cofibrations in \(G{K}/B\)  are defined by a
left lifting property, the following is true.
